Is 59 a Sophie Germain prime?

Is 59 a Sophie Germain prime?

Similarly, Sophie Germain primes may be used in the generation of pseudo-random numbers. Thus “suitable” prime numbers q are 7, 23, 47, 59, 167, 179, etc. (OEIS: A000353) (corresponding to p = 3, 11, 23, 29, 83, 89, etc.)

Where can I find Sophie Germain primes?

If both p and 2p+1 are prime, then p is a Sophie Germain prime. The first few such primes are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, and 131. Around 1825 Sophie Germain proved that the first case of Fermat’s last theorem is true for odd Germain primes.

Is 397 a Germain prime?

Yes, 397 is a prime number. The number 397 is divisible only by 1 and the number itself. For a number to be classified as a prime number, it should have exactly two factors. Since 397 has exactly two factors, i.e. 1 and 397, it is a prime number.

What is Sophie Germain identity?

An identity named after the famous french mathematician Sophie Germain (1776 – 1831) is a useful tool for math olympians: a^{4} + 4b^{4} = (a^{2}+2b^{2}-2ab)(a^{2}+2b^{2}+2ab). Here’s a problem that is easily solved with Sophie Germain’s identity: Is 2015^{4}+4^{2015} prime?

What is Sophie Germain famous for?

Sophie Germain was a revolutionary. She battled against the social prejudices of the era and a lack of formal training in order to become a celebrated mathematician. She is best known for her work in number theory, but her work in the theory of elasticity is also very important to mathematics.

Why is Sophie Germain famous?

Are there infinite Fermat primes?

There are infinitely many primes. Proof. There are infinitely many distinct Fermat numbers, each of which is divisible by an odd prime, and since any two Fermat numbers are relatively prime, these odd primes must all be distinct. Thus, there are infinitely many primes.

Why did Sophie Germain pretend to be a man?

Lived 1776 – 1831. Sophie Germain was a wholly self-taught mathematical genius who began her career pretending to be a man, because the social conventions of her time prevented women from following intellectual careers.

What is the largest known Fermat prime?

Factorization of Fermat numbers

F0	=	3 is prime
F4	=	65,537 is the largest known Fermat prime
F5	=	4,294,967,297
		641 × 6,700,417 (fully factored 1732)
F6	=	18,446,744,073,709,551,617 (20 digits)

What did Sophie Germain win?

Germain tried again and received an honorable mention for her next entry, but it had too many errors to succeed. She tried a third time and, on January 8, 1816, she was awarded the enormously prestigious Paris Academy of Sciences Prize, a one kilogram gold medal. Germain, now 39, was the first woman to win one.

Is the number P A Sophie Germain prime?

In number theory, a prime number p is a Sophie Germain prime if 2 p + 1 is also prime. The number 2 p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime.

Which is the last term in a Sophie Germain chain?

Just as every term except the last one of a Cunningham chain of the first kind is a Sophie Germain prime, so every term except the first of such a chain is a safe prime. Safe primes ending in 7, that is, of the form 10 n + 7, are the last terms in such chains when they occur, since 2 (10 n + 7) + 1 = 20 n + 15 is divisible by 5.

How did Sophie Germain prove Fermat’s theorem?

Sophie Germain primes are mentioned in the stage play Proof and the subsequent film. Specifically, Germain proved that the first case of Fermat’s Last Theorem, in which the exponent divides one of the bases, is true for every Sophie Germain prime, and she used similar arguments to prove the same for all other primes up to 100.

Who are the authors of the safe prime?

On 2 Dec 2019, Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé, and Paul Zimmermann announced the computation of a discrete logarithm modulo the 240-digit (795 bit) prime RSA-240 + 49204 (the first safe prime above RSA-240) using a number field sieve algorithm; see Discrete logarithm records .